Apparatus for extracting power from a fluid flow

ABSTRACT

A device for extracting energy from underwater fluid flows, comprising at least one fluid formation directing device ( 10 ) defining a constricted channel ( 20 ) arranged to cause fluid entering it to accelerate. A conduit ( 30 ) in fluid communication with a constricted portion of the channel ( 20 ) such that fluid is caused to flow in the conduit ( 30 ) in response to fluid flow through the channel ( 20 ). The conduit ( 30 ) can be connected to a fluid drivable engine ( 40 ) which can be positioned remotely from the channel ( 20 ), the fluid flow through the conduit ( 30 ) acting to drive the fluid drivable engine ( 40 ).

This invention relates to devices for extracting power from a fluidflow, such as a tidal stream, and structures for pumping fluids inresponse to such a flow.

With increasing public awareness of environmental pollution and inparticular, global warming there is a growing interest in renewableenergy sources. A 1994 survey of the energy available in sea or rivercurrents and tidal streams around the UK by the Department of Trade andIndustry's renewable energy unit at Harwell [see publication reference1], found that a considerable fraction of the UK's energy needs could bemet if this energy could be harnessed.

The energy in the currents is kinetic rather than potential, which meansthat it has to be extracted in a different way from that employed in aconventional hydroelectric scheme. Typically, in a tidal streaminstallation, a turbine might be placed underwater in the tidal streamto extract the energy—an underwater equivalent of a wind powergenerator. For example, in a development funded by the EC [2], it isplanned to set up submarine propeller driven turbines in selectedlocations where the current flows rapidly

A disadvantage of these conventional underwater systems is that in orderto access the energy of the fluid flow the moving parts are placedunderwater in a hostile environment making them prone to damage andinconvenient and costly to access and repair. Furthermore, if the wateris slowed too much (i.e. too big a fraction of the kinetic energy isextracted), then the head needed to drive it will be increased. Tominimise the required head, thereby obviating the need for a barrage,any turbine placed in the stream will have to have its blades highlyfeathered, making it uneconomic.

According to one aspect of the present invention there is provided anapparatus for extracting power from a fluid flow, the apparatuscomprising at least one fluid directing formation formed to define achannel having a flow accelerating constriction shaped such that fluidin the channel is caused to accelerate as it flows through the flowaccelerating constriction of the channel; a fluid drivable enginedisposed at a position exterior to the channel; a conduit disposed toprovide fluid communication between the fluid drivable engine and aportion of the channel having an accelerated fluid flow, the fluiddrivable engine being arranged such that fluid flow along the conduitacts to drive the fluid drivable engine.

The apparatus of the present invention alleviates the disadvantages ofthe prior art by providing a way of using the underwater fluid flow topump fluid away from the flow so that it can be led to a fluid drivableengine, such as a turbine, sited at position remote from the underwaterfluid flow. This can avoid moving parts underwater and thecorrespondingly high maintenance costs. Furthermore, a controllablefraction of the power in any fluid flow can be extracted. It should benoted that the apparatus will function on any scale and as such isadaptable to many different situations. This property enables the systemto be produced as modules that can be combined or used alone dependingon circumstances. A further advantage of this apparatus is its lowenvironmental impact: as much of the infrastructure is underwater theonly visible signs are the fluid drivable engine housing and pylonsbringing the power cables.

Although the conduit can be disposed in any portion of the channelhaving accelerated fluid flow, preferably it is sited in a portion ofthe channel formed to provide a maximum fluid velocity. This arrangementprovides for increased efficiency of the apparatus.

In preferred embodiments, the at least one channel is substantiallysymmetrical about a plane mid-way between its ends. Although anasymmetrical channel is possible, and may even be preferable forextracting power particularly, from a one way flow, a symmetricalchannel allows a single construction to be used for extracting power inboth directions from a two way flow, such as a tidal flow.

Advantageously, the interior surface defining the channel is generallycurved. A curved profile decreases the losses due to turbulence therebyallowing a greater flow velocity for the same head of fluid.

In an alternative embodiment, a fluid reservoir and a fluidcommunication path between the fluid drivable engine and the fluidreservoir are provided. Although in some embodiments, fluid may beexpelled from the conduit and exit via the fluid drivable engine, and inothers the suction from the conduit may be used to suck air through thefluid drivable engine, in this alternative embodiment a fluid reservoiris provided so that fluid is sucked from the fluid reservoir passesthrough the fluid drivable engine and is expelled via the conduit intothe channel

In preferred embodiments, the at least one fluid directing formation isarranged to define a plurality of channels arranged in parallel andhaving a corresponding plurality of conduits. The channels can bearranged in parallel in a single fluid directing formation or,alternatively, a plurality of fluid directing formations defining aplurality of channels can be arranged in parallel across the fluid flow.A plurality of channels arranged in parallel within the fluid flow allowan increase in the power extracted from a fluid flow. In additionmultiplexing is simple; pipe connections to all fast streams in thevicinity can be connected in parallel to drive a single fluid drivableengine, thereby achieving economy of scale. Alternatively, a pluralityof fluid drivable engines can each be arranged in fluid communicationwith a corresponding conduit and channel.

A multiplexed arrangement such as that described above allows smallquantities of power to be extracted from a widely distributed area. Thisobviates the need for a large head of water, conventionally produced bya dam. Furthermore, the extraction of small quantities of power over alarge area reduces the impact on existing eco-systems..

In some embodiments, a centrifugal pump having a fluid inlet and lowvelocity and high velocity fluid outlets is arranged in the channel suchthat the fluid-inlet receives fluid flowing through the channel, the lowvelocity fluid outlet being arranged to return fluid to the channel andthe high velocity fluid outlet being arranged to expel fluid into theconduit. Thus, in this embodiment fluid exits via the conduit ratherthan being sucked into it.

Preferably, a generally flat circular drum with a fluid channelcomprising a helix is arranged to receive fluid flowing through thechannel such that fluid entering the drum forms a swirling disk and aportion of the fluid is expelled into the conduit. This arrangementallows fluid to be expelled into the conduit, without the provision ofmoving parts that are liable to wear and need servicing, within thefluid flow.

Advantageously, the circular drum has a double wedge shaped crosssection, such that the cross section is wider at the outer circumferencethan it is in the middle section. This arrangement increases viscousdrag in the central region and decreases the formation of vortices. Inan alternative embodiment vortex formation is reduced by concentricvanes on the inside of the drum.

In preferred embodiments, the apparatus for extracting power comprises:at least two containers arranged in parallel in a fluid flow pathbetween the channel and the fluid drivable engine, each containercomprising a replenishment valve allowing fluid communication betweenthe interior and exterior of the container; and an isolation valvearrangement such that the fluid communication between individualcontainers and the channel and fluid drivable engine can be inhibited,so that when a fluid contained in one container that is in fluidcommunication with the channel and fluid drivable engine is exhaustedthe isolation valve arrangement is operable to temporarily inhibit thefluid communication between the channel and fluid drivable engine viathat container so that the container can be replenished using thereplenishment valve. This embodiment allows an alternative fluid to thatpresent in the fluid flow to flow between the tanks and the fluiddrivable engine and to drive the fluid drivable engine. Thus, a fluidwith a lower viscous drag than the fluid of the flow can be used to flowbetween the fluid drivable engine and tanks, reducing losses in thesystem. This is particularly important if the fluid drivable engine islocated at some distance from the fluid flow as may be the case in, forexample, tidal flows if the fluid drivable engine is located on shore.Furthermore, if the system is driving a gas turbine this arrangementacts to produce a reduced exhaust pressure for the gas turbine whichincreases its efficiency. It should be noted that this system is highlycompatible with a gas turbine generator in which hydrocarbons are usedto supplement, say tidal energy.

According to another aspect of the device there is provided a structureoperable to pump fluid in response to underwater fluid flow, comprisingat least one fluid directing formation formed to define a channel havinga flow accelerating constriction shaped such that fluid in the channelis caused to accelerate as it flows through the low acceleratingconstriction of the channel; a conduit disposed to provide fluidcommunication between a portion of the channel having an acceleratedfluid flow and a point exterior to the channel.

The structure of the present invention alleviates the disadvantages ofthe prior art by providing a way of using the underwater fluid flow topump fluid away from the flow so that it can be led to a site remotefrom the flow, possibly an on shore site.

Embodiments of the present invention will now be described, by way ofexample only, with reference to the accompanying drawings, in which:

FIG. 1 illustrates the profile of an angular and smooth structure havinga constricted channel;

FIG. 2 illustrates the head of water needed to achieve a given speed forthe two channels shown in FIG. 1;

FIG. 3 illustrates an apparatus for extracting power from a fluid flowaccording to an embodiment of the invention;

FIG. 4 illustrates a plurality of structures each comprising aconstricted channel and conduit connecting the constricted channels toeach other and to an external pipe;

FIG. 5 illustrates a centrifugal pump activated by a low pressure streamof water;

FIG. 6 illustrates a self-acting centrifugal pump;

FIG. 7 illustrate the cross section of the self-acting centrifugal pumpof FIG. 6;

FIG. 8 illustrates the fluid communication means, turbine and buffertanks of an embodiment of the invention; and

FIG. 9 illustrates an apparatus for extracting power from a fluid flowaccording to an embodiment of the present invention.

FIGS. 1 and 2 relate to the technological background of the presentinvention, whereas FIGS. 3 to 8 relate to embodiments of the presentinvention.

FIG. 10 is a schematic view of a pipe.

FIG. 11 is a diagram representation of height H.

FIG. 12 is a diagram relating to the extraction of energy due tosuction.

FIG. 13 is a view of a centrifungal pump.

FIG. 14 is a diagram relating to conservation equations.

With reference to FIG. 1, a structure 10 providing a constricted channel20 is illustrated schematically. The solid line represents a schematicdiagram of an angular constricted channel 20 whereas the dotted linerepresents the smoothed version. The flow of fluid through narrowchannels in which viscous forces are dominant and in which streamlineflow is maintained are predicted by Bernoulli's theorem, wherein v²+ρghis constant. This means that provided no energy is lost through frictionor in any other way, the effective pressure ρgh will go down as thespeed increases. This principle forms the basis of a Venturi flow ratemeter.

Laminar flow only occurs in tubes at relatively low velocities and withrelatively small diameters, thus in a system with large flow ratesturbulent flow will prevail. Even if the flow through a constriction isturbulent, the pressure still falls as the bulk velocity rises, asdescribed by Bernoulli's equation. This is because, to conserve waterthe flow must accelerate as the tube narrows. Therefore a force has tobe exerted on it, by pressure difference between the narrow and wideparts of the tube. A simple calculation (Appendix 1) and directexperiment shows that the pressure difference needed is that describedby Bernoulli for streamline flow. Thus it seems that a pressurereduction is associated for turbulent flow just as for streamline flow.

Turbulent flow involves energy loss, so a head of water is required toforce a fluid through a pipe. The more streamlined the pipe, the lessturbulent the flow, so the design of a pipe affects the head of waterneeded to create flow. FIG. 2, illustrates the head of water (in mm) onthe vertical axis and the velocity squared (in m² S²) on the horizontalaxis of water flowing through the smooth and angular channelsillustrated in FIG. 1. The steeper line representing flow through theangular channel. As is clear from FIG. 2, the shape of the constrictedchannel influences the head of water needed to achieve a given speed.Thus, a smoothed constriction produces a larger flow of water for agiven pressure drop. Clearly, a reduction of turbulent losses isimportant to the design of the device, as it produces a correspondingreduction in the head of water needed to produce satisfactory operation.Similarly the matching of the device to the particular conditionsavailable, must form an important part of any practical application ofthis invention.

FIG. 3, illustrates an apparatus for extracting power from a fluid flowaccording to an embodiment of the invention. In this device concretestructures 10 are sunk onto the bed of, for example, a tidal estuary.These are shaped to form a constricted channel 20. The dimensions of theconcrete structure and constricted channel are typically an inletdiameter of about 10 m, a length of about 30 m, and a constricteddiameter of 3 m. A pipe 30 from the surface of the sea is introducedinto the centre of the high speed flow region of the channel. This pipeconnects to a turbine 40 and then passes back into the sea. A turbine istaken, for the purpose of this document, to be any type of machine inwhich the kinetic energy of a moving fluid is converted into mechanicalenergy. The suction effect as described above (albeit in turbulentconditions), causes a pressure drop at the outlet of the pipe 30 withinthe channel 20. If water is allowed to flow down the pipe 30, then, inthe absence of losses due to viscosity or turbulence, the speed of themain current through the channel 20 will remain unchanged; the potentialenergy lost by the free fall of the water from the surface down the pipe30, driven in addition by atmospheric pressure from behind, will exactlyequal its kinetic energy at the bottom, so that it will join the channelcurrent with the same speed v₁. In fact, in this hypothetical situationno energy will have been gained or lost. Overall, water has come fromthe surface at v₁ and eventually been transferred to the depths at v₁, -convection has in effect occurred.

If however, the water in pipe 30 is made to do work on the way, then theresistance to flow will be increased, the speed of the fluid stream willbe reduced and energy will be extracted from the submarine current.Thus, by making the water in the pipe do work by, for example, drivingturbine 40, power can be generated at a place remote from the underwatercurrent such as on shore. The placing of the turbine on shore makes itconvenient for servicing access and subject to less extreme conditionsthan it would be underwater.

FIG. 9 illustrates an embodiment in which an apparatus for extractingpower includes an underwater fluid flow and at least a portion of the atleast one fluid directing formation, such as structure 10, is locatedunderwater. The apparatus further comprises a floating structure 41 withthe fluid drivable engine 40 being disposed on the floating structure41.

The fact that turbulent flow produces pressure reduction analogous tothat produced by laminar flow means that large flow rates of water canbe used in the device of the present invention. The data illustrated inFIG. 2 show that for an efficient system a smoothed profile for theconstricted channel 20 is preferred.

The slowing down of the channel current by the introduction of waterdown the pipe 30 from the surface will result in an increase of pressureon the outlet side. In order for the system to work, the pressuredifference between the two ends of the channel 20 through the concretestructure 10 must exceed this increase. Thus a limit is set to thequantity of water that can be sucked down the pipe by the head of wateravailable. In a tidal flow the maximum head available is of the order ofthe height of the tide.

Appendix 2 shows that a power output of 1.5 MW requires a hydrostaticpressure of 10 cm in the 30 m length of the concrete submarinestructures over and above that needed to force the water through thechannel at 20 m/s in the absence of power extraction. This is anadditional water gradient of 3 m in 1 km which is not unusual.Alternatively, the extra height differential of 10 cm could be createdlocally if a line of concrete structures formed a submarine barrage.

In the embodiment shown in FIG. 3, the constricted channel 20 issymmetrical and the conduit 30 can be rotated, for example, by the waterflow itself, such that the outlet can face either channel opening. Thismakes the structure suitable for extracting energy from fluids flowingin either direction in the constricted channel 20 and thus can be usedto extract energy from flows that periodically change direction such astidal flows. Embodiments of the invention designed to be used, forexample, in one way fluid flows may have asymmetrical constrictedchannels. Asymmetric channels may also be used in some situations fortwo way flows. This is because streamline structures are not reversibleand thus for maximum power extraction efficiency a channel speciallyshaped for streamlined flow in a particular direction may be preferred.Thus, in some situations it may be advantageous to provide separatedifferently shaped channels for the two flow directions. A disadvantageof doing this is an increase in the capital cost associated withproviding the additional channels.

In the embodiment shown, the channel 20 is formed within the concretestructure 10. An alternative in which two concrete structures form aconstricted channel, the structures possibly being modified bridgesupports is also possible. In certain situations, such as in shallowestuaries, the channels may also be formed from a “picket fence” typestructure.

FIG. 4, illustrates a front elevation of a plurality of structures 10with constricted channels 20 arranged in parallel within a fluid flow. Aplurality of conduits 30 are arranged to connect the constricted portionof each channel 20 together and then to a single turbine 40. Thus, theportion of the energy extracted from a stream can be increased, and agreater flow produced to drive the turbine 40. Such an arrangement couldbe sited across, for example, a tidal estuary so that energy could beefficiently harnessed from across a wide flow. In another embodiment, aplurality of turbines 40 are placed in fluid communication with eachconduit 30.

In alternative embodiments, the fluid flow is used to expel fluid fromthe conduit rather than sucking it into it.

It is clear that an underwater flow such as a tidal stream could be madeto drive a centrifugal pump. A “water wheel” type device, for example,could be placed in a narrow portion of the channel and be used to drivea centrifugal pump mounted on the same axis. As a further refinement,the water wheel and pump could be combined into one unit as shownschematically in FIG. 5. In the device of FIG. 5, the vanes of the pump50 are driven round by the fast water inflow, and a fraction of thetotal water throughput, say 10%. is taken off at the edge of the drumwhere both the pressure and the speed are high.

It is clear from FIG. 5 that, if the water enters at high speed and lowpressure through pipe 60, it will have a similar speed and higherpressure, due to centrifugal force, when it reaches the entrance to theperipheral take off pipe 65. If some water, say 10% of the total flow,is allowed to flow out through pipe 65, the remaining flow will exit ata lower speed through outlet pipe 70. A small fraction of the water hasthereby obtained a high speed and pressure at the expense of theremainder slowing down.

The vanes have the effect of forcing the water to rotate as though itwere a solid.

Appendices 2 and 3 give calculations showing fluid acceleration in acentrifugal pump and conservation of fluid and momentum when a fractionof the flow is bled off. If we consider water being compelled to movearound a vertical axis with uniform angular velocity ω and that itsvelocity at the outer perimeter is v₂. Due to so called “centrifugalforce”, there will be a radial pressure gradient from the hub to the rimof the disk of the liquid. A simple integration (Appendix 2) shows thatthis gives a pressure difference between the hub and rim of 2ρgh. Thepressure on the inside of the outer surface of the circular drum musttherefore be at least equal to this. In other words, the centrifugalforce compensates for the loss in pressure predicted by Bernoulli'sequation when the water speeds up from 2 m/s to 20 m/s as it negotiatesthe throttle. This means that, at the periphery of the drum, a stream offluid, a fraction of the fluid flowing through the constriction can bebled off at a pressure of at least 2ρgh and a speed of 20 m/s. If anunderwater water flow such as a tidal flow is being considered, thestream of fluid can be bled off and led via a suitable pipe to sealevel. The fluid flow should arrive at sea level at a speed of 20 m/sand at least at atmospheric pressure. If its speed is reduced, itspressure will increase correspondingly.

In another embodiment the mechanical intermediary (the vanes of FIG. 5)can be omitted and the fluid persuaded to act as its own centrifugalpump.

FIG. 6 illustrates a flat circular drum 80, split and twisted slightlyto form a helix. This forces the fluid to form a swirling disc similarto that formed by the pump of FIG. 5, but without any mechanical movingparts.

If viscous forces are dominant then the fluid would move through thecircular drum 80 as though it were a solid disc. If, however, viscousforces are not dominant then vortices form to conserve angular momentum.This has the effect of speeding up the flow near the centre of the discand slowing it down at the periphery—the opposite of what is needed.

In order to circumvent this problem a drum with a wedge shapedcross-section, as illustrated in FIG. 7, may be used. This increasesviscous effects near the centre, where the surfaces of the drum areclose together, and decrease them at larger radii, while stillmaintaining the radial pressure gradient. Another option would be to fitconcentric vanes on the insides and top and bottom surfaces of the drumto inhibit flow vectors which incorporate a radial component. As theexact form of radial velocity gradient is not too critical, aself-driven centrifugal pump may possess a wide range of such mechanicalconfigurations.

FIG. 8 illustrates the fluid communication means, turbine and buffertanks of an embodiment of the invention. In this embodiment buffer tanks90, 91 are located between the conduit 30 and turbine 40. These tanks90, 91 are located underwater near to the underwater fluid flow. Fluidcommunication means 95 connect these tanks to the turbines. Valve 100connect alternate tanks 90, 91 to the conduit 30 and turbine 40, suchthat water is sucked from a full tank 90 through the conduit 30 into thechannel 20; air flows through the turbine 40 and fluid communicationmeans to replace the water flowing from the tank 90. When this tank 90is empty of water and full of air, the valve 100 switches such that theother tank 91 that is full of water becomes connected to the conduit 30and water is sucked from this other tank 91. While this tank 91 isemptying valve 100 on tank 90 opens to allow this tank to fill withwater. Other valve means (not shown) on the tank are opened to allow theair to be exhausted. This arrangement means that instead of waterflowing between the turbine 40 and underwater fluid flow, air flows forsome of this distance. Thus, if the turbine 40 is located on shore at aremote distance from the underwater flow, the tanks can be arranged suchthat the majority of the distance is covered by the air flow and thusviscous losses caused by fluid flow between the turbine 40 and theunderwater structure are reduced.

In conclusion, calculations have shown that a stream of water can bemade available on the shore with a flow rate of 14 m/s and a pressuredifferential of about 2 atmospheres, neglecting friction and viscosityfrom an offshore current flowing at 2 m/s at a depth of about 9 m (30feet). All that is required to achieve this is a structure, preferablyconcrete, that can be manufactured in a shipyard and sunk on site, andthrough which appropriately shaped channels have been sculpted, togetherwith the necessary connecting pipes. A concrete structure has theadvantage of being buoyant when water is pumped out of it, allowing itto be floated for cleaning or for relocation to another site.

Publication References

1. 1994 survey of the energy available in currents and tidal streamsaround the UK by the DTI's renewable energy unit at Harwell (ETSUT/f05/00155/REP).

2. 1996, Fraenkel et al., “Power of Motion in the Ocean”, Anjana Ahuja,The Times Jul. 10, 1998.

APPENDIX 1 Justification of “Simple calculation”

Consider the movement of a molecule of mass within the pipe as shown inFIG. 10.

The equation of continuity states that:

A₂v=A₃u

As A₂>A₃ then u>v. Hence the kinetic energy of the molecule willincrease from (½)mv² to (½)mu².

To conserve energy, the potential energy of the molecule must havedeceased, i.e. the molecule must have “fallen” through a height H (seeFIG. 11) where:${mgH} = {\frac{1}{2}{m\left( {u^{2} - v^{2}} \right)}}$

In a liquid, the height through which a molecule can “fall” is increasedas the local pressure is reduced. Hence the pressure at the end of thepipe is an amount ρgh lower than at the entrance to the pipe.

Hence we have that:${\frac{1}{2}{\rho \left( {u^{2} - v^{2}} \right)}} = {\rho \quad {g\left( {h_{1} - h_{2}} \right)}}$

as required.

APPENDIX 2 Extraction of energy due to suction (see FIG. 12)

where: v₂>v₃ and so the pressure at outlet has increased by an amountρgh;

h=head of water needed to drive the water through

Sum of areas: (1)

A ₂ +a=A ₃

Conservation of water: (2)

A ₂v₂+au=A₃ v₃

Conservation of energy (3)${{\frac{v_{2}^{2}}{2g}\left( {A_{2}v_{2}} \right)} + {\frac{u_{2}^{2}}{2g}({au})}} = {\left\{ {\frac{v_{3}^{2}}{2g} + h} \right\} A_{3}v_{3}}$

Using (1) and (2) to eliminate v₃ and A₃, then: (4),${{\frac{v_{2}^{2}}{2g}\left( {A_{2}v_{2}} \right)} + {\frac{u_{2}^{2}}{2g}({au})}} = {{\frac{1}{2g}\left\{ \frac{\left( {{A_{2}v_{2}} + {au}} \right)^{3}}{\left( {A_{2} + a} \right)^{2}} \right\}} + {h\left( {{A_{2}v_{2}} + {au}} \right)}}$

Putting A₂=10a simplifies (4) to: (5)

0.2v ₂ ³+0.02u ³+0.01v ₂ ₃+0.1u ³=0.3v ₂ ² u+0.03u ² v ₂+2gh(1.1)² (v₂+0.1u)

Suppose that the velocity, u in the insert is some fraction, β of theinlet velocity, V₂. i.e.: (6)

u=βv₂

Then (5) becomes: (7)

0.12β³−0.03β²−0.3012β+0.198=0

Let

0.12β³−0.03β²−0.3012β+0.198=X

and find the value of β for which X is close to zero. Using numericalmethods it is found that β=0.8 when X≅0.

Suppose that the velocity into the inlet, v₂ is 20 ms⁻¹ then thevelocity in the insert, u is 16 ms⁻¹ from (6).

The energy per unit time (i.e. power) extracted from the system is:$P = {{{\frac{1}{2}v_{2}^{2}\frac{A_{2}}{10}\left( {v_{2}\left( {1 - \beta} \right)} \right)^{3}}\therefore P} = {{\frac{1}{2} \cdot 1000 \cdot (0.7) \cdot (20)^{3} \cdot \left( {1 - (0.8)^{3}} \right)} = {1.43\quad {MW}}}}$

is obtained from a device with an inlet diameter of 10 m and a pipethrottle of diameter 3 m and area A₂=π.(1.5)².

N.B. This is the head needed to supply the power calculated above. Agreater head of water will be needed to overcome turbulent flow.

APPENDIX 3: Centrifungal Pump (See FIG. 13).

Caption: A disk of water, inner radius R₀, outer radius R, rotating atangular velocity ω has a pressure differential between its centre andcircumference.

Water in a cylindrical container, height h, inner radius R₀, outerradius R, is rotating at angular velocity ω. The mass of liquid in athin cylinder height h and thickness dr at radius r is

dm=2πtρhdr

The centrifugal force exerted by this is dF=rω²dm. Hince the outwardpressure across dr is

dP=dF/2πrh=ρrω²dr

Integration of this between R₀ and R shows that there is a pressuredifference between the inner and outer walls of the container equal to${P_{R} - P_{R_{0}}} = {\rho \quad \omega^{2}\frac{\left( {R^{2} - R_{0}^{2}} \right)}{2}}$

So, if R>>R₀,${P_{R} - P_{R_{0}}} = {{{\rho\omega}^{2}\frac{R^{2}}{2}} = {\frac{\rho \quad v^{2}}{2}\quad \left( {{{if}\quad \omega \quad R} = v} \right)}}$

According to Bernoulli's theorem, the total energy content of the watermust be conserved, provided it is flowing along a streamline path. Wehave achieved this by slowing down the water near the centre of thedisk, and using the kinetic energy so released to increase the pressureat the circumference. Furthermore, we can say that if the kinetic energycontent of the water in the rotating disk has come predominantly fromits hydrostatic content when flowing into the venturi at a low speed,then, according to Bernoulli's equation,

v²/2g=H

where ρgH is the hydrostatic pressure. Hence, as P_(RO) cannot be lessthan zero, the pressure at the circumference of the cylinder should besimilar to the hydrostatic pressure of the water at the point at whichit enters the venturi.

APPENDIX 4: CONSERVATION EQUATIONS

The caption for FIG. 14 is as follows: The water enters the centralsection of the venturi at speed v₂. We suppose that a fraction is bledoff at speed u, and that the speed at which the remainder exits thecentral section of the venturi is v₃.

Area of the pipe, and area of main exit pipe is A₂. Area of bleed pipeto shore is a. The hydrostatic pressure is ρgh at the venturi inlet andoutlet, where h≅0, and ρgH at the side tube.

1. CONSERVE WATER

A ₂v₂ =A ₂ v ₃ +au

so

a=A ₂(v ₂ −v ₃)/u (1)

provided V₃<V₂.

2 CONSERVE ENERGY

In other words, ensure that power in=power out. So, for unit mass ofwater, $\begin{matrix}{{\left( {\frac{v_{2}^{2}}{2g} + h} \right)A_{2}v_{2}} = {{\left( {\frac{v_{3}^{2}}{2g} + H} \right)A_{2}v_{3}} + {\left( {\frac{u^{2}}{2g} + H} \right){au}}}} \\{= {{\left( {\frac{v_{3}^{2}}{2g} + H} \right)A_{2}v_{3}} + {\left( {\frac{u^{2}}{2g} + H} \right){A_{2}\left( {v_{2} - v_{3}} \right)}}}}\end{matrix}$

using (1). Hence${\frac{\left( {v_{2}^{3} - v_{3}^{3}} \right)}{2g} + {h\left( {v_{2} - v_{3}} \right)}} = {\left( {\frac{u^{2}}{2g} + H} \right)\left( {v_{2} - v_{3}} \right)}$

Therefore, provided v₂ does not equal v₃, we obtain (2)$\left( {\frac{u^{2}}{2g} + H} \right) = {h + \frac{\left( {v_{2}^{2} + {v_{2}v_{3}} + v_{3}^{2}} \right)}{2g}}$

What does this mean in practice? It means that provided the localpressure near the bleed off tube can be increased to H (by invokingcentrifugal force, for instance), then the relationship expressed by theabove equation can be satisfied.

3. EXAMPLE

For example, make the area of the bleed off pipe 10% of that of the maincentral venturi tube, so a=A₂/10. This defines the geometry, and meansthat u=10(v₂-v₃). In addition, let v₃=9v₂/10. This defines the qualityof kinetic energy that has been removed from the main flow. So,

u=v₂ and to satisfy equation (2)

H-h=0.85v₂ ²/2 g

We have already seen from Appendix 1 that centrifugal forces can be usedto raise the equivalent depth to v₂ ²/2 g.

To put this another way, if water can be forced out of the side tube bycentrifugal force, then, depending on the effective value achieved forH, v₃/v₂ will fall to the fraction defined by equation (2).

What is claimed is:
 1. An apparatus for extracting power from a waterflow, the apparatus comprising: at least one at least partiallyunderwater fluid directing formation formed to define a channel having aflow accelerating constriction shaped such that water flows through thechannel and is caused to accelerate as it flows through the flowaccelerating constriction of the channel; a fluid drivable enginedisposed at a position exterior to the channel; a conduit disposed toprovide fluid communication between the fluid drivable engine, an openend of said conduit extending into said flow accelerating constrictionand a portion of the channel having an accelerated fluid flow, the fluiddrivable engine being arranged such that fluid flow along the conduitcaused by reduced pressure at said open end of the said conduit acts todrive the fluid drivable engine.
 2. An apparatus for extracting poweraccording to claim 1, wherein the conduit is arranged to provide fluidcommunication between the fluid drivable engine and a portion of thechannel formed to provide a maximum fluid velocity.
 3. An apparatus forextracting power according to claims 1 or 2, wherein the exterior of thechannel in a fluid flow direction is enclosed by the at least one fluiddirecting formation and an inlet of the channel has a larger crosssectional area than a central section of the channel.
 4. An apparatusfor extracting power according to claim 1, wherein the at least onechannel is substantially symmetrical about a plane mid-way between itsends.
 5. An apparatus for extracting power according to claim 1, whereinthe interior surface defining the channel is generally curved.
 6. Anapparatus for extracting power according to claim 1, wherein the conduitis flexible.
 7. An apparatus for extracting power according to claim 1,comprising a fluid reservoir and a fluid communication path between thefluid drivable engine and the fluid reservoir.
 8. An apparatus forextracting power according to claim 1, comprising an electricitygenerator, the generator being arranged to be driven by the fluiddrivable engine.
 9. An apparatus for extracting power according to claim1, the apparatus further comprising a floating structure, the fluiddrivable engine being disposed on the floating structure.
 10. Anapparatus for extracting power according to claim 1, wherein the atleast one fluid directing formation is arranged to define a plurality ofchannels arranged in parallel, having a corresponding plurality ofconduits.
 11. An apparatus for extracting power according to claim 10,wherein the plurality of conduits are arranged in fluid communicationwith each other and with the fluid drivable engine.
 12. An apparatus forextracting power according to claim 10, wherein the apparatus forextracting power comprises a plurality of fluid drivable engines, eachin fluid communication with a corresponding conduit and channel.
 13. Anapparatus for extracting power according to claim 1, comprising acentrifugal pump having a fluid inlet and low velocity and high velocityfluid outlets, the pump being arranged within the channel such that thefluid inlet receives fluid flowing through the channel, the low velocityfluid outlet being arranged to return fluid to the channel and the highvelocity fluid being arranged to expel fluid into the conduit.
 14. Anapparatus for extracting power according to claim 1, comprising agenerally flat circular drum with a fluid channel comprising a helix,the drum being arranged to receive fluid flowing through the channel andcomprising a fluid outlet arranged in fluid communication with theconduit, such that fluid entering the drum forms a swirling disk and aportion of the fluid is expelled into the conduit.
 15. An apparatus forextracting power according to claim 14, wherein the circular drum has adouble wedge shaped cross section, such that the cross section is widerat the outer circumference than it is in the middle section.
 16. Anapparatus for extracting power according to claim 14, wherein thegenerally flat circular drum comprises concentric vanes inside the drum.17. An apparatus for extracting power according to claim 1, theapparatus for extracting power comprising: at least two containersarranged in parallel in a fluid flow path between the channel and thefluid drivable engine, each container comprising a replenishment valveallowing fluid communication between the interior and exterior of thecontainer; and an isolation valve arrangement such that the fluidcommunication between individual containers and the channel and fluiddrivable engine can be inhibited, so that when a fluid contained in onecontainer that is in fluid communication with the channel and fluiddrivable engine is exhausted the isolation valve arrangement is operableto temporarily inhibit the fluid communication between the channel andfluid drivable engine via that container so that the container can bereplenished using the replenishment valve.
 18. A structure operable topump fluid in response to underwater fluid flow, comprising at least onefluid directing formation formed to define a channel having a flowaccelerating constriction shaped such that fluid in the channel iscaused to accelerate as it flows through the flow acceleratingconstriction of the channel; and a conduit disposed to provide fluidcommunication between a portion of the channel having an acceleratedfluid flow and a point exterior to the channel, an open end of saidconduit extending into said flow accelerating constriction.
 19. Anapparatus for extracting power from a water flow, the apparatuscomprising: at least one at least partially underwater fluid directingformation formed to define a channel having a flow acceleratingconstriction shaped such that water flows through the channel and iscaused to accelerate as it flows through the flow acceleratingconstriction of the channel; a fluid drivable engine disposed at aposition exterior to the channel; a floating structure, the fluiddrivable engine being disposed on the floating structure; and a conduitdisposed to provide fluid communication between the fluid drivableengine and a portion of the channel having an accelerated fluid flow,the fluid drivable engine being arranged such that fluid flow along theconduit acts to drive the fluid drivable engine.